Highest weight vectors of irreducible representations of the quantum superalgebra Uq(gl(m,n))
Abstract
The Iwahori-Hecke algebra of type A acts on tensor product space of the natural representation of the quantum superalgebra Uq(gl(m,n)). We show this action of the Hecke algebra and the action of Uq(gl(m,n)) on the same space determine commuting actions of each other. Together with this result and Gyoja's q-analogue of the Young symmetrizer, we construct a highest weight vector of each irreducible summmand of the tensor product space.
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